Question: Solve for $x$ and $y$ using substitution. ${-5x-4y = 1}$ ${y = -4x-3}$
Since $y$ has already been solved for, substitute $-4x-3$ for $y$ in the first equation. ${-5x - 4}{(-4x-3)}{= 1}$ Simplify and solve for $x$ $-5x+16x + 12 = 1$ $11x+12 = 1$ $11x+12{-12} = 1{-12}$ $11x = -11$ $\dfrac{11x}{{11}} = \dfrac{-11}{{11}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -4x-3}\thinspace$ to find $y$ ${y = -4}{(-1)}{ - 3}$ $y = 4 - 3$ $y = 1$ You can also plug ${x = -1}$ into $\thinspace {-5x-4y = 1}\thinspace$ and get the same answer for $y$ : ${-5}{(-1)}{ - 4y = 1}$ ${y = 1}$